A physical factor that is known to limit the accuracy in a fiber optical resonator gyroscope (FOG) is non-linear Kerr effect. This nonlinear effect, that is a nonlinear phase shift dependent on the intensities of the clockwise (cw) and counterclockwise light waves propagating in the resonator, is accumulated by the two light signals while being transmitted via an optic fiber. This effect, generated by the Kerr effect in silica glass, can produce a large round-trip phase difference between the two waves, and therefore an erroneous indication of rotation rate in the fiber optical resonator gyro.
The non-linear Kerr effect, for a light wave propagating in a single direction, gives an effective index of refraction coefficient of a material that changes with then=n0+K|E|2  (1)where K is a constant of proportionality containing the Kerr coefficient of the medium, E is electric field intensity.
In a fiber optical resonator gyro, since light is traveling in both directions, the propagation constants β1 and β2 experienced by the clockwise (cw) and counterclockwise (ccw) propagating lightwaves, respectively, at a point z along the fiber length can be expressed as:β1=β0+Δβ[I1(z)+2I2(z)],  (2)β2=β0+Δβ[2I1(z)+I2(z)],  (3)where the above assumes the two lightwaves are linearly-polarized along the axis. Here β0 is the propagation constant common to both waves (related to no via β0=2πno/λ, where λ is the free space light wavelength) and where Δβ is the constant of proportionality of the change in the propagation constant related to the optical power in the fiber and contains the Kerr coefficient of the material. Note that the propagation constants in the two directions are different if the intensity of the clockwise wave, I1(z)=U1*U1 and the intensities of the counterclockwise wave I2(z)=U2*U2 are different. Here U1 and U2 represent the electric fields of the lightwaves at a single frequency of light. In this case, this means that a difference in phase shift (non-reciprocal phase shift) will be accumulated between cw and ccw waves in a stretch of medium propagation through a segment of the medium with an intensity difference. In the fiber optic resonator gyroscope, unequal intensities in the resonator in the cw and ccw directions give a non-reciprocal round trip phase shift, and therefore a resonant frequency difference, that erroneously indicates the presence of rotation rate. In other words, the erroneous rotation rate is due to an accumulation of phase shifts by cw and ccw waves and a phase shift between cw and ccw waves due to the Kerr Effect, or a non-linear phase shift accumulation in the closed path of the optical resonator.